Patent GB-777451-A (GB)
Title: Improvements in and relating to computers of the analogue kind
IPC: G06G7/34
Filed: 1953-12-18
Abstract: 777,451. Electric analogue calculating systems. GENERAL ELECTRIC CO. Dec. 18, 1953 [Dec. 20, 1952], No. 35329/53. Class 37. An electric analogue computer for solving an array of linear simultaneous equations comprises a Wheatstone bridge having in one arm a plurality of inert series-resistance or parallel conductance networks, each controlled by first and second numerically corresponding switch groups responsive to the coefficients and unknowns of the product terms of one side of an equation to insert resistance or conductance values analogous to the several product terms, and in a second adjacent arm a resistance variable to insert a resistance or conductance analogous to the constant term of the other side of such equation; the bridge being completed by a pair of constant resistance arms, an unbalance indicator and an electrical excitation source whereby the array of equations may be solved by successively balancing the bridge in application of the error iteration, Gauss- Seidel, or matrix inversion methods of approximation. Fig. 2 shows a bridge network of which arm 16 comprises a variable resistance and adjacent arm 15 comprises plural multiplier networks M1 to MN of the kind described in Specification 749,556, comprising plural chains of series resistances (Fig. 1, not shown) selectively switchable to short-circuit corresponding resistances of each chain in response to one variable and to short-circuit each chain itself in response to another variable, whereby the total network resistance represents the product of the two variables; and is inserted in series in such arm. The bridge is completed by equal constant resistance arms 17, 18 and provided with an indicating instrument 19 across one diagonal and an energization voltage source across the other diagonal. To solve the array of simultaneous linear equations the coefficients a 11 to a 1 n of the first equation are respectively set into one input of each corresponding. multiplier network M1 to MN, and approximations to the unknowns X 1  to Xn are similarly set in to the remaining multiplier inputs, while resistance 16 is set to represent the constant term C 1  The value of X 1  is manipulated to rebalance the bridge, and the first equation is then satisfied for the prevailing values of X 1  to Xn, after which coefficients a 21  to a 2 n and constant C 2  are similarly set into the bridge with the previous values of X 1  to Xn, and X 2  is manipulated to balance the bridge and satisfy the second equation. This procedure is repeated for the coefficients a 31  to a 3 n, constant C 3  and unknown X 3 , and similarly repeated for all the subsequent equations of the array, until no further variations of the successive unknowns X 1  to Xn are necessary to achieve balance, after insertion of any subsequent set of coefficients and corresponding constant term, an 1  to ann, and C n . The array is then solved for the unknowns X 1  to Xn. Fig. 3 shows a more complete form of the apparatus wherein the variable resistance arm comprises a bank of plural resistances 16 of different values preset to represent the several values of the required constants C 1  to Cn, which are selectible therefrom by a push-button switch arrangement 20 for insertion either in multiplier arm 15 or adjacent arm 16 by double throw reversing switches 21 operable to take account of the signs of the constant terms represented by the resistance values. The input factors of the multiplier networks constituting arm 15 are inserted by switching control knobs 25 responsive to the respective unknowns X 1  to Xn and by switching relays 22 controlled in accordance 'with the respective coefficients a 11  to ann by known punched card code reading mechanism, while double throw cross-connected reversing switches 23, 24 set in accordance with the sign of the coefficients and the unknowns determine the sign of each product term by energizing relay 22 to connect the associated multiplier in either arm 15 or 16 of the bridge as required. The bridge completed by equal resistances 17, 18 is energized by rectified A.C. across one diagonal while unbalance across the other is detected by galvanometer 27 shunted by an overload protection rectifier 28. The coefficients of successive equations are set up by the successive insertion of corresponding punched cards in the reading apparatus which operates relays 22 to insert the desired coefficients into the corresponding multipliers and the constant term values are inserted by selecting successive preset resistance values by switches 21; the signs being determined by switches 21, 23, 24 so that the array of equations is soluble as set forth above. In a modification (Fig. 5, not shown) the multiplier arm of the bridge comprises a plurality of parallel multiplying networks as described in Specification 749,556, each comprising two groups of plural transversely related insulated conductors (Fig. 4, not shown) connected at their points of intersection by resistances of predetermined and graduated values, wherein a conductor is selectible from each group by two banks of switches respectively operable in response to the appropriate coefficient and unknown of the equation array so as to introduce into the bridge arm a combination of resistances in parallel such that the conductance of each network is proportional to its associated product term and the total conductance inserted is proportional to the sum of the product terms on one side of the appropriate equation of the array. Fig. 6 shows a more cornplete form of the modified apparatus wherein plural multipliers M1 to M12 of the kind described, are connected in one arm of the bridge, correspondingly to the several product terms of each equation; one bank of input switches being controlled by a punch card reading mechanism 40 in response to the coefficient values a 11  to ann and the other bank being controlled either manually or by relay controlled motors responsive to bridge unbalance in response to the unknowns X 1  to Xn. The adjacent arm 16 comprises a bank of individually predetermined resistances selectible by push-button operated switches 42 in correspondence with the constant terms C 1  to Cn of the array of equations, and the bridge is completed by equal resistances 17, 18, is energized by rectified A.C. across one diagonal, and has connected across the other diagonal an unbalance detecting galvanometer 19 in shunt with an overload protection rectifier 43. The equations are soluble by error iteration as set forth above. To avoid errors in the computation due to spurious currents flowing through indirect shunt paths formed in the multiplying conductance networks (Fig. 4, not shown), each individual switch of one input switch bank of each multiplier has a pair of auxiliary contacts operable complementarity with its main contacts whereby each unused intersection of the associated conductor group not connected over the main contacts to the network output, is supplied over conductors 46a with a compensation voltage from the slider of a potentiometer 47 energized from the bridge supply which is adjusted by a servo-system 49, 51 to reduce to zero the effective voltage at the potentiometer slider and thus balance out the effect of the spurious currents; such balance being indicated by galvanometer 48 shunted by overload protection rectifiers. Procedures are described whereby the more accurate solution of the array of equations may be obtained from the apparatus by employing the Gauss-Seidel method, or alternatively transforming the array for direct arithmetical solution for the unknowns using  the matrix inversion method.